Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6840,2,Mod(1,6840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6840.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6840 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6840.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(54.6176749826\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2280) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.470683\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6840.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.30777 | −1.25022 | −0.625110 | − | 0.780536i | \(-0.714946\pi\) | ||||
−0.625110 | + | 0.780536i | \(0.714946\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.24914 | −0.678141 | −0.339071 | − | 0.940761i | \(-0.610113\pi\) | ||||
−0.339071 | + | 0.940761i | \(0.610113\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.19051 | −0.884888 | −0.442444 | − | 0.896796i | \(-0.645888\pi\) | ||||
−0.442444 | + | 0.896796i | \(0.645888\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.55691 | −0.862678 | −0.431339 | − | 0.902190i | \(-0.641959\pi\) | ||||
−0.431339 | + | 0.902190i | \(0.641959\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.55691 | −0.324639 | −0.162320 | − | 0.986738i | \(-0.551898\pi\) | ||||
−0.162320 | + | 0.986738i | \(0.551898\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.24914 | −0.789046 | −0.394523 | − | 0.918886i | \(-0.629090\pi\) | ||||
−0.394523 | + | 0.918886i | \(0.629090\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.43965 | −1.33620 | −0.668100 | − | 0.744071i | \(-0.732892\pi\) | ||||
−0.668100 | + | 0.744071i | \(0.732892\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.30777 | 0.559116 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.30777 | −0.872593 | −0.436296 | − | 0.899803i | \(-0.643710\pi\) | ||||
−0.436296 | + | 0.899803i | \(0.643710\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.36641 | −0.369571 | −0.184785 | − | 0.982779i | \(-0.559159\pi\) | ||||
−0.184785 | + | 0.982779i | \(0.559159\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.80605 | 0.580418 | 0.290209 | − | 0.956963i | \(-0.406275\pi\) | ||||
0.290209 | + | 0.956963i | \(0.406275\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.55691 | 1.39402 | 0.697010 | − | 0.717062i | \(-0.254513\pi\) | ||||
0.697010 | + | 0.717062i | \(0.254513\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.94137 | 0.563052 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.55691 | 0.488580 | 0.244290 | − | 0.969702i | \(-0.421445\pi\) | ||||
0.244290 | + | 0.969702i | \(0.421445\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.24914 | 0.303274 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.498281 | −0.0648707 | −0.0324353 | − | 0.999474i | \(-0.510326\pi\) | ||||
−0.0324353 | + | 0.999474i | \(0.510326\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.17590 | −0.150559 | −0.0752793 | − | 0.997162i | \(-0.523985\pi\) | ||||
−0.0752793 | + | 0.997162i | \(0.523985\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.19051 | 0.395734 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.9966 | −1.58778 | −0.793891 | − | 0.608060i | \(-0.791948\pi\) | ||||
−0.793891 | + | 0.608060i | \(0.791948\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.3810 | 1.23200 | 0.616000 | − | 0.787746i | \(-0.288752\pi\) | ||||
0.616000 | + | 0.787746i | \(0.288752\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.117266 | −0.0137250 | −0.00686249 | − | 0.999976i | \(-0.502184\pi\) | ||||
−0.00686249 | + | 0.999976i | \(0.502184\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.43965 | 0.847827 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.1725 | 1.33610 | 0.668051 | − | 0.744116i | \(-0.267129\pi\) | ||||
0.668051 | + | 0.744116i | \(0.267129\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.55691 | 0.385802 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.6302 | −1.12679 | −0.563397 | − | 0.826186i | \(-0.690506\pi\) | ||||
−0.563397 | + | 0.826186i | \(0.690506\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.5535 | 1.10630 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.68879 | 0.780678 | 0.390339 | − | 0.920671i | \(-0.372358\pi\) | ||||
0.390339 | + | 0.920671i | \(0.372358\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.38101 | −0.833942 | −0.416971 | − | 0.908920i | \(-0.636908\pi\) | ||||
−0.416971 | + | 0.908920i | \(0.636908\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.76547 | −0.371023 | −0.185511 | − | 0.982642i | \(-0.559394\pi\) | ||||
−0.185511 | + | 0.982642i | \(0.559394\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.11727 | 0.591378 | 0.295689 | − | 0.955284i | \(-0.404451\pi\) | ||||
0.295689 | + | 0.955284i | \(0.404451\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.4948 | −1.48414 | −0.742068 | − | 0.670324i | \(-0.766155\pi\) | ||||
−0.742068 | + | 0.670324i | \(0.766155\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.94137 | 0.841133 | 0.420567 | − | 0.907262i | \(-0.361831\pi\) | ||||
0.420567 | + | 0.907262i | \(0.361831\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.55691 | 0.145183 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.7655 | 1.07854 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.94137 | −0.540124 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.1173 | −0.897762 | −0.448881 | − | 0.893591i | \(-0.648177\pi\) | ||||
−0.448881 | + | 0.893591i | \(0.648177\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.51633 | 0.132482 | 0.0662410 | − | 0.997804i | \(-0.478899\pi\) | ||||
0.0662410 | + | 0.997804i | \(0.478899\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.30777 | 0.286820 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.8827 | 1.01521 | 0.507605 | − | 0.861590i | \(-0.330531\pi\) | ||||
0.507605 | + | 0.861590i | \(0.330531\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.4983 | 1.39937 | 0.699683 | − | 0.714453i | \(-0.253325\pi\) | ||||
0.699683 | + | 0.714453i | \(0.253325\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.17590 | 0.600079 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.24914 | 0.352872 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.23109 | 0.592394 | 0.296197 | − | 0.955127i | \(-0.404281\pi\) | ||||
0.296197 | + | 0.955127i | \(0.404281\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.67418 | −0.299001 | −0.149500 | − | 0.988762i | \(-0.547766\pi\) | ||||
−0.149500 | + | 0.988762i | \(0.547766\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.43965 | 0.597567 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.381015 | 0.0304083 | 0.0152041 | − | 0.999884i | \(-0.495160\pi\) | ||||
0.0152041 | + | 0.999884i | \(0.495160\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.14992 | 0.405871 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.80949 | 0.220056 | 0.110028 | − | 0.993928i | \(-0.464906\pi\) | ||||
0.110028 | + | 0.993928i | \(0.464906\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.17590 | 0.555288 | 0.277644 | − | 0.960684i | \(-0.410446\pi\) | ||||
0.277644 | + | 0.960684i | \(0.410446\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.82066 | −0.216974 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.94137 | 0.375685 | 0.187843 | − | 0.982199i | \(-0.439851\pi\) | ||||
0.187843 | + | 0.982199i | \(0.439851\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.30777 | −0.250044 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.61555 | −0.195495 | −0.0977476 | − | 0.995211i | \(-0.531164\pi\) | ||||
−0.0977476 | + | 0.995211i | \(0.531164\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.6121 | −1.30910 | −0.654549 | − | 0.756020i | \(-0.727141\pi\) | ||||
−0.654549 | + | 0.756020i | \(0.727141\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.30777 | 0.390235 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.00000 | 0.585018 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.7440 | −0.849765 | −0.424882 | − | 0.905249i | \(-0.639685\pi\) | ||||
−0.424882 | + | 0.905249i | \(0.639685\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.574960 | −0.0413865 | −0.0206933 | − | 0.999786i | \(-0.506587\pi\) | ||||
−0.0206933 | + | 0.999786i | \(0.506587\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.5569 | 0.823396 | 0.411698 | − | 0.911320i | \(-0.364936\pi\) | ||||
0.411698 | + | 0.911320i | \(0.364936\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.50172 | 0.248230 | 0.124115 | − | 0.992268i | \(-0.460391\pi\) | ||||
0.124115 | + | 0.992268i | \(0.460391\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.0552 | 0.986481 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.36641 | 0.165277 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.24914 | 0.155576 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.23109 | 0.635495 | 0.317747 | − | 0.948175i | \(-0.397074\pi\) | ||||
0.317747 | + | 0.948175i | \(0.397074\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.80605 | −0.259571 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.6087 | 1.67055 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.3484 | 0.763373 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.9931 | 1.20491 | 0.602454 | − | 0.798153i | \(-0.294190\pi\) | ||||
0.602454 | + | 0.798153i | \(0.294190\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.94480 | 0.394571 | 0.197285 | − | 0.980346i | \(-0.436787\pi\) | ||||
0.197285 | + | 0.980346i | \(0.436787\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.1725 | 0.936543 | 0.468271 | − | 0.883585i | \(-0.344877\pi\) | ||||
0.468271 | + | 0.883585i | \(0.344877\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.3484 | 0.874480 | 0.437240 | − | 0.899345i | \(-0.355956\pi\) | ||||
0.437240 | + | 0.899345i | \(0.355956\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.55691 | −0.623424 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.2423 | 1.56810 | 0.784051 | − | 0.620697i | \(-0.213150\pi\) | ||||
0.784051 | + | 0.620697i | \(0.213150\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.2311 | −0.723458 | −0.361729 | − | 0.932283i | \(-0.617814\pi\) | ||||
−0.361729 | + | 0.932283i | \(0.617814\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.94137 | −0.251805 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.19051 | 0.203007 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.48024 | 0.472148 | 0.236074 | − | 0.971735i | \(-0.424139\pi\) | ||||
0.236074 | + | 0.971735i | \(0.424139\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.50172 | 0.220151 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.0551953 | −0.00344299 | −0.00172149 | − | 0.999999i | \(-0.500548\pi\) | ||||
−0.00172149 | + | 0.999999i | \(0.500548\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.5569 | 1.09093 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.93793 | −0.242823 | −0.121412 | − | 0.992602i | \(-0.538742\pi\) | ||||
−0.121412 | + | 0.992602i | \(0.538742\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.55691 | −0.218500 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.8681 | −1.08944 | −0.544719 | − | 0.838618i | \(-0.683364\pi\) | ||||
−0.544719 | + | 0.838618i | \(0.683364\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.8466 | −1.69156 | −0.845782 | − | 0.533529i | \(-0.820865\pi\) | ||||
−0.845782 | + | 0.533529i | \(0.820865\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.24914 | −0.135628 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.9931 | −0.720597 | −0.360299 | − | 0.932837i | \(-0.617325\pi\) | ||||
−0.360299 | + | 0.932837i | \(0.617325\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.8647 | 0.648133 | 0.324066 | − | 0.946034i | \(-0.394950\pi\) | ||||
0.324066 | + | 0.946034i | \(0.394950\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.6922 | 0.992250 | 0.496125 | − | 0.868251i | \(-0.334756\pi\) | ||||
0.496125 | + | 0.868251i | \(0.334756\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.82754 | 0.462045 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.34836 | −0.255786 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −31.1690 | −1.82091 | −0.910457 | − | 0.413604i | \(-0.864270\pi\) | ||||
−0.910457 | + | 0.413604i | \(0.864270\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.498281 | 0.0290110 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.96735 | 0.287269 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.5896 | −0.725651 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.17590 | 0.0673318 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.498281 | −0.0284384 | −0.0142192 | − | 0.999899i | \(-0.504526\pi\) | ||||
−0.0142192 | + | 0.999899i | \(0.504526\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.01805 | −0.0577281 | −0.0288640 | − | 0.999583i | \(-0.509189\pi\) | ||||
−0.0288640 | + | 0.999583i | \(0.509189\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.3810 | 0.699816 | 0.349908 | − | 0.936784i | \(-0.386213\pi\) | ||||
0.349908 | + | 0.936784i | \(0.386213\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.78801 | −0.268921 | −0.134461 | − | 0.990919i | \(-0.542930\pi\) | ||||
−0.134461 | + | 0.990919i | \(0.542930\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.55691 | 0.535084 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.55691 | 0.197912 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.19051 | −0.176978 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −31.6121 | −1.74283 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.4362 | −0.683556 | −0.341778 | − | 0.939781i | \(-0.611029\pi\) | ||||
−0.341778 | + | 0.939781i | \(0.611029\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.9966 | 0.710078 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.4543 | −0.841847 | −0.420923 | − | 0.907096i | \(-0.638294\pi\) | ||||
−0.420923 | + | 0.907096i | \(0.638294\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.7328 | 0.906133 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.1173 | 0.546281 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.8241 | 0.688434 | 0.344217 | − | 0.938890i | \(-0.388144\pi\) | ||||
0.344217 | + | 0.938890i | \(0.388144\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.8793 | 1.54587 | 0.772937 | − | 0.634483i | \(-0.218787\pi\) | ||||
0.772937 | + | 0.634483i | \(0.218787\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.00000 | −0.106449 | −0.0532246 | − | 0.998583i | \(-0.516950\pi\) | ||||
−0.0532246 | + | 0.998583i | \(0.516950\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.3810 | −0.550967 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.7440 | −1.04205 | −0.521024 | − | 0.853542i | \(-0.674450\pi\) | ||||
−0.521024 | + | 0.853542i | \(0.674450\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.117266 | 0.00613800 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.6888 | 0.714549 | 0.357274 | − | 0.933999i | \(-0.383706\pi\) | ||||
0.357274 | + | 0.933999i | \(0.383706\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.7655 | −0.610833 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.1510 | 1.56116 | 0.780579 | − | 0.625057i | \(-0.214924\pi\) | ||||
0.780579 | + | 0.625057i | \(0.214924\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.5569 | 0.698217 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.6673 | −1.31844 | −0.659220 | − | 0.751950i | \(-0.729114\pi\) | ||||
−0.659220 | + | 0.751950i | \(0.729114\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.8759 | 1.22000 | 0.610000 | − | 0.792402i | \(-0.291170\pi\) | ||||
0.610000 | + | 0.792402i | \(0.291170\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.43965 | −0.379160 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −29.3484 | −1.48802 | −0.744010 | − | 0.668168i | \(-0.767079\pi\) | ||||
−0.744010 | + | 0.668168i | \(0.767079\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.53781 | 0.280059 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.1173 | −0.608148 | −0.304074 | − | 0.952648i | \(-0.598347\pi\) | ||||
−0.304074 | + | 0.952648i | \(0.598347\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.4734 | 1.37195 | 0.685977 | − | 0.727623i | \(-0.259375\pi\) | ||||
0.685977 | + | 0.727623i | \(0.259375\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.7363 | 1.18239 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.9379 | 0.591741 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.9605 | 1.62979 | 0.814895 | − | 0.579608i | \(-0.196794\pi\) | ||||
0.814895 | + | 0.579608i | \(0.196794\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.64820 | 0.0811027 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.1725 | −0.597523 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.7474 | 0.720459 | 0.360229 | − | 0.932864i | \(-0.382698\pi\) | ||||
0.360229 | + | 0.932864i | \(0.382698\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.9897 | 1.21792 | 0.608961 | − | 0.793200i | \(-0.291586\pi\) | ||||
0.608961 | + | 0.793200i | \(0.291586\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.55691 | −0.172536 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.88961 | 0.188231 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.8501 | −0.522630 | −0.261315 | − | 0.965254i | \(-0.584156\pi\) | ||||
−0.261315 | + | 0.965254i | \(0.584156\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.0371 | −0.530412 | −0.265206 | − | 0.964192i | \(-0.585440\pi\) | ||||
−0.265206 | + | 0.964192i | \(0.585440\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.55691 | 0.0744773 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.2277 | 1.44269 | 0.721344 | − | 0.692577i | \(-0.243525\pi\) | ||||
0.721344 | + | 0.692577i | \(0.243525\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.9018 | −1.04059 | −0.520294 | − | 0.853987i | \(-0.674178\pi\) | ||||
−0.520294 | + | 0.853987i | \(0.674178\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.6302 | 0.503918 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.01805 | −0.142430 | −0.0712152 | − | 0.997461i | \(-0.522688\pi\) | ||||
−0.0712152 | + | 0.997461i | \(0.522688\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.32238 | 0.250621 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.5535 | −0.494755 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.5017 | 0.631584 | 0.315792 | − | 0.948828i | \(-0.397730\pi\) | ||||
0.315792 | + | 0.948828i | \(0.397730\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.64820 | 0.169914 | 0.0849568 | − | 0.996385i | \(-0.472925\pi\) | ||||
0.0849568 | + | 0.996385i | \(0.472925\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.53887 | −0.396835 | −0.198417 | − | 0.980118i | \(-0.563580\pi\) | ||||
−0.198417 | + | 0.980118i | \(0.563580\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.5535 | −1.04365 | −0.521825 | − | 0.853052i | \(-0.674749\pi\) | ||||
−0.521825 | + | 0.853052i | \(0.674749\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 42.9897 | 1.98508 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.56035 | −0.393605 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.6267 | 1.53644 | 0.768222 | − | 0.640184i | \(-0.221142\pi\) | ||||
0.768222 | + | 0.640184i | \(0.221142\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.9345 | 0.772146 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.68879 | −0.349130 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.8466 | 0.536823 | 0.268411 | − | 0.963304i | \(-0.413501\pi\) | ||||
0.268411 | + | 0.963304i | \(0.413501\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.3269 | −1.59428 | −0.797140 | − | 0.603795i | \(-0.793655\pi\) | ||||
−0.797140 | + | 0.603795i | \(0.793655\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.1138 | 0.680693 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −34.3380 | −1.54027 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.7259 | 1.37548 | 0.687741 | − | 0.725956i | \(-0.258602\pi\) | ||||
0.687741 | + | 0.725956i | \(0.258602\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −42.1656 | −1.88007 | −0.940035 | − | 0.341077i | \(-0.889208\pi\) | ||||
−0.940035 | + | 0.341077i | \(0.889208\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.38101 | 0.372950 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −41.7440 | −1.85027 | −0.925135 | − | 0.379639i | \(-0.876048\pi\) | ||||
−0.925135 | + | 0.379639i | \(0.876048\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.387890 | 0.0171593 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.76547 | 0.165926 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.4948 | −0.945342 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.7405 | 0.821038 | 0.410519 | − | 0.911852i | \(-0.365348\pi\) | ||||
0.410519 | + | 0.911852i | \(0.365348\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.7259 | −0.643920 | −0.321960 | − | 0.946753i | \(-0.604342\pi\) | ||||
−0.321960 | + | 0.946753i | \(0.604342\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.4622 | 1.15271 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5760 | −0.894609 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.55004 | 0.327028 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.11727 | −0.264472 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.86469 | −0.381829 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.2277 | −1.72952 | −0.864761 | − | 0.502184i | \(-0.832530\pi\) | ||||
−0.864761 | + | 0.502184i | \(0.832530\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.4948 | 0.663726 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.7294 | 1.61319 | 0.806596 | − | 0.591103i | \(-0.201307\pi\) | ||||
0.806596 | + | 0.591103i | \(0.201307\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.24914 | 0.181019 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.9931 | 0.847136 | 0.423568 | − | 0.905864i | \(-0.360777\pi\) | ||||
0.423568 | + | 0.905864i | \(0.360777\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.1432 | −0.513605 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −44.0483 | −1.85642 | −0.928208 | − | 0.372063i | \(-0.878651\pi\) | ||||
−0.928208 | + | 0.372063i | \(0.878651\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.94137 | −0.376166 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.7474 | 0.702088 | 0.351044 | − | 0.936359i | \(-0.385827\pi\) | ||||
0.351044 | + | 0.936359i | \(0.385827\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.1396 | 1.51240 | 0.756198 | − | 0.654343i | \(-0.227055\pi\) | ||||
0.756198 | + | 0.654343i | \(0.227055\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.55691 | −0.0649278 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.3810 | −0.681951 | −0.340975 | − | 0.940072i | \(-0.610757\pi\) | ||||
−0.340975 | + | 0.940072i | \(0.610757\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −40.2637 | −1.67042 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.00000 | −0.331326 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.5604 | −0.518421 | −0.259211 | − | 0.965821i | \(-0.583462\pi\) | ||||
−0.259211 | + | 0.965821i | \(0.583462\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.43965 | 0.306545 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 38.9966 | 1.60140 | 0.800698 | − | 0.599068i | \(-0.204462\pi\) | ||||
0.800698 | + | 0.599068i | \(0.204462\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.7655 | −0.482337 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.3415 | −0.708554 | −0.354277 | − | 0.935141i | \(-0.615273\pi\) | ||||
−0.354277 | + | 0.935141i | \(0.615273\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.9119 | −0.649062 | −0.324531 | − | 0.945875i | \(-0.605206\pi\) | ||||
−0.324531 | + | 0.945875i | \(0.605206\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.94137 | 0.241551 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.2637 | −0.984835 | −0.492418 | − | 0.870359i | \(-0.663887\pi\) | ||||
−0.492418 | + | 0.870359i | \(0.663887\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −30.4914 | −1.23355 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −44.7259 | −1.80646 | −0.903232 | − | 0.429153i | \(-0.858812\pi\) | ||||
−0.903232 | + | 0.429153i | \(0.858812\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.6707 | 0.429588 | 0.214794 | − | 0.976659i | \(-0.431092\pi\) | ||||
0.214794 | + | 0.976659i | \(0.431092\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.3776 | 1.90427 | 0.952133 | − | 0.305685i | \(-0.0988853\pi\) | ||||
0.952133 | + | 0.305685i | \(0.0988853\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 35.1621 | 1.40874 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.8793 | 0.752767 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.4622 | 0.416493 | 0.208247 | − | 0.978076i | \(-0.433224\pi\) | ||||
0.208247 | + | 0.978076i | \(0.433224\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.1173 | 0.401491 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.5750 | −0.498238 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.6233 | −0.814571 | −0.407285 | − | 0.913301i | \(-0.633525\pi\) | ||||
−0.407285 | + | 0.913301i | \(0.633525\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.4216 | 1.35746 | 0.678728 | − | 0.734390i | \(-0.262532\pi\) | ||||
0.678728 | + | 0.734390i | \(0.262532\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.8207 | 1.01511 | 0.507557 | − | 0.861618i | \(-0.330548\pi\) | ||||
0.507557 | + | 0.861618i | \(0.330548\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.12070 | 0.0439915 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −45.3155 | −1.77333 | −0.886666 | − | 0.462410i | \(-0.846985\pi\) | ||||
−0.886666 | + | 0.462410i | \(0.846985\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.51633 | −0.0592478 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 45.3415 | 1.76625 | 0.883127 | − | 0.469134i | \(-0.155434\pi\) | ||||
0.883127 | + | 0.469134i | \(0.155434\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.6121 | −0.685032 | −0.342516 | − | 0.939512i | \(-0.611279\pi\) | ||||
−0.342516 | + | 0.939512i | \(0.611279\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.30777 | −0.128270 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.61555 | 0.256155 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.64476 | 0.102100 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.8061 | −0.532184 | −0.266092 | − | 0.963948i | \(-0.585733\pi\) | ||||
−0.266092 | + | 0.963948i | \(0.585733\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.7914 | 0.914380 | 0.457190 | − | 0.889369i | \(-0.348856\pi\) | ||||
0.457190 | + | 0.889369i | \(0.348856\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.4328 | −0.976020 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.11383 | −0.272203 | −0.136102 | − | 0.990695i | \(-0.543457\pi\) | ||||
−0.136102 | + | 0.990695i | \(0.543457\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.8827 | −0.454016 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.3484 | −0.432338 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.1465 | −0.690325 | −0.345162 | − | 0.938543i | \(-0.612176\pi\) | ||||
−0.345162 | + | 0.938543i | \(0.612176\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.4983 | −0.625815 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.41711 | 0.318821 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.9897 | −0.943847 | −0.471924 | − | 0.881639i | \(-0.656440\pi\) | ||||
−0.471924 | + | 0.881639i | \(0.656440\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.30777 | 0.200186 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.7225 | 1.04261 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.9311 | −1.19920 | −0.599598 | − | 0.800301i | \(-0.704673\pi\) | ||||
−0.599598 | + | 0.800301i | \(0.704673\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.5829 | 0.433783 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.17590 | −0.268363 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.5941 | 1.43932 | 0.719658 | − | 0.694329i | \(-0.244299\pi\) | ||||
0.719658 | + | 0.694329i | \(0.244299\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.4553 | 0.463860 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.24914 | −0.157809 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.0337 | −1.41059 | −0.705296 | − | 0.708913i | \(-0.749186\pi\) | ||||
−0.705296 | + | 0.708913i | \(0.749186\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.5378 | −0.500714 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.5275 | 0.536585 | 0.268293 | − | 0.963337i | \(-0.413541\pi\) | ||||
0.268293 | + | 0.963337i | \(0.413541\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.2311 | 1.07674 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.46563 | −0.201056 | −0.100528 | − | 0.994934i | \(-0.532053\pi\) | ||||
−0.100528 | + | 0.994934i | \(0.532053\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 44.5795 | 1.63546 | 0.817731 | − | 0.575601i | \(-0.195232\pi\) | ||||
0.817731 | + | 0.575601i | \(0.195232\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.23109 | −0.264927 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.2345 | −0.739354 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.43965 | 0.271477 | 0.135738 | − | 0.990745i | \(-0.456659\pi\) | ||||
0.135738 | + | 0.990745i | \(0.456659\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.67418 | 0.133717 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.6190 | −0.858447 | −0.429223 | − | 0.903198i | \(-0.641213\pi\) | ||||
−0.429223 | + | 0.903198i | \(0.641213\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.9966 | −0.688625 | −0.344312 | − | 0.938855i | \(-0.611888\pi\) | ||||
−0.344312 | + | 0.938855i | \(0.611888\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 51.2534 | 1.85550 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.58977 | 0.0574032 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.2311 | −0.405004 | −0.202502 | − | 0.979282i | \(-0.564907\pi\) | ||||
−0.202502 | + | 0.979282i | \(0.564907\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.0191 | −0.935842 | −0.467921 | − | 0.883770i | \(-0.654997\pi\) | ||||
−0.467921 | + | 0.883770i | \(0.654997\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.43965 | −0.267240 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.36641 | 0.0847853 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.3484 | −0.835470 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.381015 | −0.0135990 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.1984 | 0.506120 | 0.253060 | − | 0.967451i | \(-0.418563\pi\) | ||||
0.253060 | + | 0.967451i | \(0.418563\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.5760 | −1.05160 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.75172 | 0.133227 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.1725 | 1.21045 | 0.605225 | − | 0.796054i | \(-0.293083\pi\) | ||||
0.605225 | + | 0.796054i | \(0.293083\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.9931 | −1.20259 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.263748 | 0.00930748 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.14992 | −0.181511 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.1173 | −0.707285 | −0.353643 | − | 0.935381i | \(-0.615057\pi\) | ||||
−0.353643 | + | 0.935381i | \(0.615057\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.762030 | −0.0267585 | −0.0133792 | − | 0.999910i | \(-0.504259\pi\) | ||||
−0.0133792 | + | 0.999910i | \(0.504259\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.80949 | −0.0984122 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.80605 | −0.133157 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.50516 | 0.157231 | 0.0786155 | − | 0.996905i | \(-0.474950\pi\) | ||||
0.0786155 | + | 0.996905i | \(0.474950\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.1836 | −0.389837 | −0.194918 | − | 0.980819i | \(-0.562444\pi\) | ||||
−0.194918 | + | 0.980819i | \(0.562444\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.2829 | 0.566210 | 0.283105 | − | 0.959089i | \(-0.408635\pi\) | ||||
0.283105 | + | 0.959089i | \(0.408635\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.3845 | 0.534324 | 0.267162 | − | 0.963652i | \(-0.413914\pi\) | ||||
0.267162 | + | 0.963652i | \(0.413914\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.0191 | −0.485733 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.17590 | −0.248332 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.0812 | 0.555184 | 0.277592 | − | 0.960699i | \(-0.410464\pi\) | ||||
0.277592 | + | 0.960699i | \(0.410464\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.9448 | −0.377407 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.82066 | 0.0970337 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.6527 | 0.675275 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.26375 | 0.283278 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.9119 | −0.681772 | −0.340886 | − | 0.940105i | \(-0.610727\pi\) | ||||
−0.340886 | + | 0.940105i | \(0.610727\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.1364 | 0.961120 | 0.480560 | − | 0.876962i | \(-0.340433\pi\) | ||||
0.480560 | + | 0.876962i | \(0.340433\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.5760 | 1.14560 | 0.572799 | − | 0.819696i | \(-0.305857\pi\) | ||||
0.572799 | + | 0.819696i | \(0.305857\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.8724 | −1.11899 | −0.559495 | − | 0.828834i | \(-0.689005\pi\) | ||||
−0.559495 | + | 0.828834i | \(0.689005\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.94137 | −0.168012 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 41.4656 | 1.40501 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.30777 | 0.111823 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.1579 | −0.815753 | −0.407876 | − | 0.913037i | \(-0.633731\pi\) | ||||
−0.407876 | + | 0.913037i | \(0.633731\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.4914 | −1.09466 | −0.547332 | − | 0.836916i | \(-0.684356\pi\) | ||||
−0.547332 | + | 0.836916i | \(0.684356\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.3404 | 0.886426 | 0.443213 | − | 0.896416i | \(-0.353839\pi\) | ||||
0.443213 | + | 0.896416i | \(0.353839\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.996562 | −0.0334613 | −0.0167306 | − | 0.999860i | \(-0.505326\pi\) | ||||
−0.0167306 | + | 0.999860i | \(0.505326\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.4656 | 1.12240 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.55691 | −0.319810 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.61555 | 0.0874281 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31.6121 | 1.05432 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.6516 | −0.421487 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.6121 | 0.585446 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.1430 | 1.43254 | 0.716271 | − | 0.697823i | \(-0.245848\pi\) | ||||
0.716271 | + | 0.697823i | \(0.245848\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.6413 | −0.650746 | −0.325373 | − | 0.945586i | \(-0.605490\pi\) | ||||
−0.325373 | + | 0.945586i | \(0.605490\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.3776 | −0.906066 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.01567 | −0.165632 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.8827 | −1.24964 | −0.624818 | − | 0.780770i | \(-0.714827\pi\) | ||||
−0.624818 | + | 0.780770i | \(0.714827\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.1207 | −1.09018 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.30777 | −0.174519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.39133 | 0.176884 | 0.0884419 | − | 0.996081i | \(-0.471811\pi\) | ||||
0.0884419 | + | 0.996081i | \(0.471811\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.94137 | −0.129173 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.00000 | −0.261628 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.7328 | 0.873323 | 0.436661 | − | 0.899626i | \(-0.356161\pi\) | ||||
0.436661 | + | 0.899626i | \(0.356161\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.35953 | 0.142117 | 0.0710583 | − | 0.997472i | \(-0.477362\pi\) | ||||
0.0710583 | + | 0.997472i | \(0.477362\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.68429 | 0.119977 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.9379 | −1.03784 | −0.518922 | − | 0.854822i | \(-0.673666\pi\) | ||||
−0.518922 | + | 0.854822i | \(0.673666\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.374139 | 0.0121451 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.82754 | −0.0591998 | −0.0295999 | − | 0.999562i | \(-0.509423\pi\) | ||||
−0.0295999 | + | 0.999562i | \(0.509423\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.7440 | 0.380026 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −39.3054 | −1.26924 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.3484 | 0.785431 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.574960 | 0.0185086 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.926759 | −0.0298026 | −0.0149013 | − | 0.999889i | \(-0.504743\pi\) | ||||
−0.0149013 | + | 0.999889i | \(0.504743\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 58.1035 | 1.86463 | 0.932315 | − | 0.361647i | \(-0.117785\pi\) | ||||
0.932315 | + | 0.361647i | \(0.117785\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −54.5726 | −1.74952 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.02598 | 0.256774 | 0.128387 | − | 0.991724i | \(-0.459020\pi\) | ||||
0.128387 | + | 0.991724i | \(0.459020\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.9087 | 0.764126 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 44.8103 | 1.42923 | 0.714614 | − | 0.699519i | \(-0.246602\pi\) | ||||
0.714614 | + | 0.699519i | \(0.246602\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.5569 | −0.368234 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.92570 | −0.188426 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.7620 | −1.16778 | −0.583892 | − | 0.811831i | \(-0.698471\pi\) | ||||
−0.583892 | + | 0.811831i | \(0.698471\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.50172 | −0.111012 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.3741 | 0.835277 | 0.417639 | − | 0.908613i | \(-0.362858\pi\) | ||||
0.417639 | + | 0.908613i | \(0.362858\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6840.2.a.bf.1.1 | 3 | ||
3.2 | odd | 2 | 2280.2.a.s.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 4560.2.a.bv.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2280.2.a.s.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
4560.2.a.bv.1.3 | 3 | 12.11 | even | 2 | |||
6840.2.a.bf.1.1 | 3 | 1.1 | even | 1 | trivial |